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Просмотр файла: secp256k1.js
"use strict";
Object.defineProperty(exports, "__esModule", { value: true });
exports.encodeToCurve = exports.hashToCurve = exports.secp256k1_hasher = exports.schnorr = exports.secp256k1 = void 0;
/**
* SECG secp256k1. See [pdf](https://www.secg.org/sec2-v2.pdf).
*
* Belongs to Koblitz curves: it has efficiently-computable GLV endomorphism ψ,
* check out {@link EndomorphismOpts}. Seems to be rigid (not backdoored).
* @module
*/
/*! noble-curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */
const sha2_js_1 = require("@noble/hashes/sha2.js");
const utils_js_1 = require("@noble/hashes/utils.js");
const _shortw_utils_ts_1 = require("./_shortw_utils.js");
const hash_to_curve_ts_1 = require("./abstract/hash-to-curve.js");
const modular_ts_1 = require("./abstract/modular.js");
const weierstrass_ts_1 = require("./abstract/weierstrass.js");
const utils_ts_1 = require("./utils.js");
// Seems like generator was produced from some seed:
// `Point.BASE.multiply(Point.Fn.inv(2n, N)).toAffine().x`
// // gives short x 0x3b78ce563f89a0ed9414f5aa28ad0d96d6795f9c63n
const secp256k1_CURVE = {
p: BigInt('0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f'),
n: BigInt('0xfffffffffffffffffffffffffffffffebaaedce6af48a03bbfd25e8cd0364141'),
h: BigInt(1),
a: BigInt(0),
b: BigInt(7),
Gx: BigInt('0x79be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798'),
Gy: BigInt('0x483ada7726a3c4655da4fbfc0e1108a8fd17b448a68554199c47d08ffb10d4b8'),
};
const secp256k1_ENDO = {
beta: BigInt('0x7ae96a2b657c07106e64479eac3434e99cf0497512f58995c1396c28719501ee'),
basises: [
[BigInt('0x3086d221a7d46bcde86c90e49284eb15'), -BigInt('0xe4437ed6010e88286f547fa90abfe4c3')],
[BigInt('0x114ca50f7a8e2f3f657c1108d9d44cfd8'), BigInt('0x3086d221a7d46bcde86c90e49284eb15')],
],
};
const _0n = /* @__PURE__ */ BigInt(0);
const _1n = /* @__PURE__ */ BigInt(1);
const _2n = /* @__PURE__ */ BigInt(2);
/**
* √n = n^((p+1)/4) for fields p = 3 mod 4. We unwrap the loop and multiply bit-by-bit.
* (P+1n/4n).toString(2) would produce bits [223x 1, 0, 22x 1, 4x 0, 11, 00]
*/
function sqrtMod(y) {
const P = secp256k1_CURVE.p;
// prettier-ignore
const _3n = BigInt(3), _6n = BigInt(6), _11n = BigInt(11), _22n = BigInt(22);
// prettier-ignore
const _23n = BigInt(23), _44n = BigInt(44), _88n = BigInt(88);
const b2 = (y * y * y) % P; // x^3, 11
const b3 = (b2 * b2 * y) % P; // x^7
const b6 = ((0, modular_ts_1.pow2)(b3, _3n, P) * b3) % P;
const b9 = ((0, modular_ts_1.pow2)(b6, _3n, P) * b3) % P;
const b11 = ((0, modular_ts_1.pow2)(b9, _2n, P) * b2) % P;
const b22 = ((0, modular_ts_1.pow2)(b11, _11n, P) * b11) % P;
const b44 = ((0, modular_ts_1.pow2)(b22, _22n, P) * b22) % P;
const b88 = ((0, modular_ts_1.pow2)(b44, _44n, P) * b44) % P;
const b176 = ((0, modular_ts_1.pow2)(b88, _88n, P) * b88) % P;
const b220 = ((0, modular_ts_1.pow2)(b176, _44n, P) * b44) % P;
const b223 = ((0, modular_ts_1.pow2)(b220, _3n, P) * b3) % P;
const t1 = ((0, modular_ts_1.pow2)(b223, _23n, P) * b22) % P;
const t2 = ((0, modular_ts_1.pow2)(t1, _6n, P) * b2) % P;
const root = (0, modular_ts_1.pow2)(t2, _2n, P);
if (!Fpk1.eql(Fpk1.sqr(root), y))
throw new Error('Cannot find square root');
return root;
}
const Fpk1 = (0, modular_ts_1.Field)(secp256k1_CURVE.p, { sqrt: sqrtMod });
/**
* secp256k1 curve, ECDSA and ECDH methods.
*
* Field: `2n**256n - 2n**32n - 2n**9n - 2n**8n - 2n**7n - 2n**6n - 2n**4n - 1n`
*
* @example
* ```js
* import { secp256k1 } from '@noble/curves/secp256k1';
* const { secretKey, publicKey } = secp256k1.keygen();
* const msg = new TextEncoder().encode('hello');
* const sig = secp256k1.sign(msg, secretKey);
* const isValid = secp256k1.verify(sig, msg, publicKey) === true;
* ```
*/
exports.secp256k1 = (0, _shortw_utils_ts_1.createCurve)({ ...secp256k1_CURVE, Fp: Fpk1, lowS: true, endo: secp256k1_ENDO }, sha2_js_1.sha256);
// Schnorr signatures are superior to ECDSA from above. Below is Schnorr-specific BIP0340 code.
// https://github.com/bitcoin/bips/blob/master/bip-0340.mediawiki
/** An object mapping tags to their tagged hash prefix of [SHA256(tag) | SHA256(tag)] */
const TAGGED_HASH_PREFIXES = {};
function taggedHash(tag, ...messages) {
let tagP = TAGGED_HASH_PREFIXES[tag];
if (tagP === undefined) {
const tagH = (0, sha2_js_1.sha256)((0, utils_ts_1.utf8ToBytes)(tag));
tagP = (0, utils_ts_1.concatBytes)(tagH, tagH);
TAGGED_HASH_PREFIXES[tag] = tagP;
}
return (0, sha2_js_1.sha256)((0, utils_ts_1.concatBytes)(tagP, ...messages));
}
// ECDSA compact points are 33-byte. Schnorr is 32: we strip first byte 0x02 or 0x03
const pointToBytes = (point) => point.toBytes(true).slice(1);
const Pointk1 = /* @__PURE__ */ (() => exports.secp256k1.Point)();
const hasEven = (y) => y % _2n === _0n;
// Calculate point, scalar and bytes
function schnorrGetExtPubKey(priv) {
const { Fn, BASE } = Pointk1;
const d_ = (0, weierstrass_ts_1._normFnElement)(Fn, priv);
const p = BASE.multiply(d_); // P = d'⋅G; 0 < d' < n check is done inside
const scalar = hasEven(p.y) ? d_ : Fn.neg(d_);
return { scalar, bytes: pointToBytes(p) };
}
/**
* lift_x from BIP340. Convert 32-byte x coordinate to elliptic curve point.
* @returns valid point checked for being on-curve
*/
function lift_x(x) {
const Fp = Fpk1;
if (!Fp.isValidNot0(x))
throw new Error('invalid x: Fail if x ≥ p');
const xx = Fp.create(x * x);
const c = Fp.create(xx * x + BigInt(7)); // Let c = x³ + 7 mod p.
let y = Fp.sqrt(c); // Let y = c^(p+1)/4 mod p. Same as sqrt().
// Return the unique point P such that x(P) = x and
// y(P) = y if y mod 2 = 0 or y(P) = p-y otherwise.
if (!hasEven(y))
y = Fp.neg(y);
const p = Pointk1.fromAffine({ x, y });
p.assertValidity();
return p;
}
const num = utils_ts_1.bytesToNumberBE;
/**
* Create tagged hash, convert it to bigint, reduce modulo-n.
*/
function challenge(...args) {
return Pointk1.Fn.create(num(taggedHash('BIP0340/challenge', ...args)));
}
/**
* Schnorr public key is just `x` coordinate of Point as per BIP340.
*/
function schnorrGetPublicKey(secretKey) {
return schnorrGetExtPubKey(secretKey).bytes; // d'=int(sk). Fail if d'=0 or d'≥n. Ret bytes(d'⋅G)
}
/**
* Creates Schnorr signature as per BIP340. Verifies itself before returning anything.
* auxRand is optional and is not the sole source of k generation: bad CSPRNG won't be dangerous.
*/
function schnorrSign(message, secretKey, auxRand = (0, utils_js_1.randomBytes)(32)) {
const { Fn } = Pointk1;
const m = (0, utils_ts_1.ensureBytes)('message', message);
const { bytes: px, scalar: d } = schnorrGetExtPubKey(secretKey); // checks for isWithinCurveOrder
const a = (0, utils_ts_1.ensureBytes)('auxRand', auxRand, 32); // Auxiliary random data a: a 32-byte array
const t = Fn.toBytes(d ^ num(taggedHash('BIP0340/aux', a))); // Let t be the byte-wise xor of bytes(d) and hash/aux(a)
const rand = taggedHash('BIP0340/nonce', t, px, m); // Let rand = hash/nonce(t || bytes(P) || m)
// Let k' = int(rand) mod n. Fail if k' = 0. Let R = k'⋅G
const { bytes: rx, scalar: k } = schnorrGetExtPubKey(rand);
const e = challenge(rx, px, m); // Let e = int(hash/challenge(bytes(R) || bytes(P) || m)) mod n.
const sig = new Uint8Array(64); // Let sig = bytes(R) || bytes((k + ed) mod n).
sig.set(rx, 0);
sig.set(Fn.toBytes(Fn.create(k + e * d)), 32);
// If Verify(bytes(P), m, sig) (see below) returns failure, abort
if (!schnorrVerify(sig, m, px))
throw new Error('sign: Invalid signature produced');
return sig;
}
/**
* Verifies Schnorr signature.
* Will swallow errors & return false except for initial type validation of arguments.
*/
function schnorrVerify(signature, message, publicKey) {
const { Fn, BASE } = Pointk1;
const sig = (0, utils_ts_1.ensureBytes)('signature', signature, 64);
const m = (0, utils_ts_1.ensureBytes)('message', message);
const pub = (0, utils_ts_1.ensureBytes)('publicKey', publicKey, 32);
try {
const P = lift_x(num(pub)); // P = lift_x(int(pk)); fail if that fails
const r = num(sig.subarray(0, 32)); // Let r = int(sig[0:32]); fail if r ≥ p.
if (!(0, utils_ts_1.inRange)(r, _1n, secp256k1_CURVE.p))
return false;
const s = num(sig.subarray(32, 64)); // Let s = int(sig[32:64]); fail if s ≥ n.
if (!(0, utils_ts_1.inRange)(s, _1n, secp256k1_CURVE.n))
return false;
// int(challenge(bytes(r)||bytes(P)||m))%n
const e = challenge(Fn.toBytes(r), pointToBytes(P), m);
// R = s⋅G - e⋅P, where -eP == (n-e)P
const R = BASE.multiplyUnsafe(s).add(P.multiplyUnsafe(Fn.neg(e)));
const { x, y } = R.toAffine();
// Fail if is_infinite(R) / not has_even_y(R) / x(R) ≠ r.
if (R.is0() || !hasEven(y) || x !== r)
return false;
return true;
}
catch (error) {
return false;
}
}
/**
* Schnorr signatures over secp256k1.
* https://github.com/bitcoin/bips/blob/master/bip-0340.mediawiki
* @example
* ```js
* import { schnorr } from '@noble/curves/secp256k1';
* const { secretKey, publicKey } = schnorr.keygen();
* // const publicKey = schnorr.getPublicKey(secretKey);
* const msg = new TextEncoder().encode('hello');
* const sig = schnorr.sign(msg, secretKey);
* const isValid = schnorr.verify(sig, msg, publicKey);
* ```
*/
exports.schnorr = (() => {
const size = 32;
const seedLength = 48;
const randomSecretKey = (seed = (0, utils_js_1.randomBytes)(seedLength)) => {
return (0, modular_ts_1.mapHashToField)(seed, secp256k1_CURVE.n);
};
// TODO: remove
exports.secp256k1.utils.randomSecretKey;
function keygen(seed) {
const secretKey = randomSecretKey(seed);
return { secretKey, publicKey: schnorrGetPublicKey(secretKey) };
}
return {
keygen,
getPublicKey: schnorrGetPublicKey,
sign: schnorrSign,
verify: schnorrVerify,
Point: Pointk1,
utils: {
randomSecretKey: randomSecretKey,
randomPrivateKey: randomSecretKey,
taggedHash,
// TODO: remove
lift_x,
pointToBytes,
numberToBytesBE: utils_ts_1.numberToBytesBE,
bytesToNumberBE: utils_ts_1.bytesToNumberBE,
mod: modular_ts_1.mod,
},
lengths: {
secretKey: size,
publicKey: size,
publicKeyHasPrefix: false,
signature: size * 2,
seed: seedLength,
},
};
})();
const isoMap = /* @__PURE__ */ (() => (0, hash_to_curve_ts_1.isogenyMap)(Fpk1, [
// xNum
[
'0x8e38e38e38e38e38e38e38e38e38e38e38e38e38e38e38e38e38e38daaaaa8c7',
'0x7d3d4c80bc321d5b9f315cea7fd44c5d595d2fc0bf63b92dfff1044f17c6581',
'0x534c328d23f234e6e2a413deca25caece4506144037c40314ecbd0b53d9dd262',
'0x8e38e38e38e38e38e38e38e38e38e38e38e38e38e38e38e38e38e38daaaaa88c',
],
// xDen
[
'0xd35771193d94918a9ca34ccbb7b640dd86cd409542f8487d9fe6b745781eb49b',
'0xedadc6f64383dc1df7c4b2d51b54225406d36b641f5e41bbc52a56612a8c6d14',
'0x0000000000000000000000000000000000000000000000000000000000000001', // LAST 1
],
// yNum
[
'0x4bda12f684bda12f684bda12f684bda12f684bda12f684bda12f684b8e38e23c',
'0xc75e0c32d5cb7c0fa9d0a54b12a0a6d5647ab046d686da6fdffc90fc201d71a3',
'0x29a6194691f91a73715209ef6512e576722830a201be2018a765e85a9ecee931',
'0x2f684bda12f684bda12f684bda12f684bda12f684bda12f684bda12f38e38d84',
],
// yDen
[
'0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffefffff93b',
'0x7a06534bb8bdb49fd5e9e6632722c2989467c1bfc8e8d978dfb425d2685c2573',
'0x6484aa716545ca2cf3a70c3fa8fe337e0a3d21162f0d6299a7bf8192bfd2a76f',
'0x0000000000000000000000000000000000000000000000000000000000000001', // LAST 1
],
].map((i) => i.map((j) => BigInt(j)))))();
const mapSWU = /* @__PURE__ */ (() => (0, weierstrass_ts_1.mapToCurveSimpleSWU)(Fpk1, {
A: BigInt('0x3f8731abdd661adca08a5558f0f5d272e953d363cb6f0e5d405447c01a444533'),
B: BigInt('1771'),
Z: Fpk1.create(BigInt('-11')),
}))();
/** Hashing / encoding to secp256k1 points / field. RFC 9380 methods. */
exports.secp256k1_hasher = (() => (0, hash_to_curve_ts_1.createHasher)(exports.secp256k1.Point, (scalars) => {
const { x, y } = mapSWU(Fpk1.create(scalars[0]));
return isoMap(x, y);
}, {
DST: 'secp256k1_XMD:SHA-256_SSWU_RO_',
encodeDST: 'secp256k1_XMD:SHA-256_SSWU_NU_',
p: Fpk1.ORDER,
m: 1,
k: 128,
expand: 'xmd',
hash: sha2_js_1.sha256,
}))();
/** @deprecated use `import { secp256k1_hasher } from '@noble/curves/secp256k1.js';` */
exports.hashToCurve = (() => exports.secp256k1_hasher.hashToCurve)();
/** @deprecated use `import { secp256k1_hasher } from '@noble/curves/secp256k1.js';` */
exports.encodeToCurve = (() => exports.secp256k1_hasher.encodeToCurve)();
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